A002508 Expansion of a modular function for Gamma_0(6). (Formerly M1910 N0754)

1, -2, 9, -4, 28, 18, 118, 80, 504, 466, 1631, 2160, 5466, 7498, 17658, 25088, 51944, 78660, 149099, 226544, 412920, 627830, 1090006, 1671840, 2796805, 4263984, 6969690, 10555224, 16836620, 25396506, 39699240, 59409184, 91460952, 135795598, 205951071, 303740496, 454672142

Offset

3,2

References

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Vaclav Kotesovec, Table of n, a(n) for n = 3..1000

Morris Newman, Construction and application of a class of modular functions (II). Proc. London Math. Soc. (3) 9 1959 373-387.

Morris Newman, Construction and application of a class of modular functions, II, Proc. London Math. Soc. (3) 9 1959 373-387. [Annotated scanned copy, barely legible]

Formula

eta(z)^2*eta(6z)^22/(eta(2z)^10*eta(3z)^14).

Euler transform of period 6 sequence [ -2, 8, 12, 8, -2, 0, ...]. - Michael Somos, Nov 10 2005

a(n) ~ exp(2*Pi*sqrt(2*n/3)) / (2^(27/4) * 3^(17/4) * n^(3/4)). - Vaclav Kotesovec, Apr 09 2018

Mathematica

QP = QPochhammer; s = QP[q]^2*QP[q^6]^22/(QP[q^2]^10*QP[q^3]^14) + O[q]^40; CoefficientList[s, q] (* Jean-François Alcover, Nov 30 2015, adapted from PARI *)

Prog

(PARI) {a(n)=local(A); if(n<3, 0, n-=3; A=x*O(x^n); polcoeff( eta(x+A)^2*eta(x^6+A)^22/ eta(x^2+A)^10/eta(x^3+A)^14, n))} /* Michael Somos, Nov 10 2005 */

Crossrefs

Reciprocal series to A002507. Cf. A002509.

Sequence in context: A302451 A220416 A054789 * A353242 A249596 A038215

Adjacent sequences: A002505 A002506 A002507 * A002509 A002510 A002511

Keyword

sign,easy

Author

N. J. A. Sloane

Extensions

More terms from Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Jan 14 2001

Status

approved